Answer:
[tex]tan(\frac{\pi}{2})=\frac{1}{0}[/tex]
Step-by-step explanation:
The given expression is
[tex]tan(\frac{\pi}{2})[/tex]
We know that the tangent function is defined as the quotient between the sin and cosin functions, that is
[tex]tan(\theta)=\frac{sin\theta}{cos \theta}[/tex], where [tex]\theta = \frac{\pi }{2}[/tex]
So, if we use this trigonometric expression, we have
[tex]tan(\frac{\pi}{2})=\frac{sin(\frac{\pi}{2} )}{cos(\frac{\pi}{2}) }[/tex]
But, [tex]\frac{\pi}{2}=90\°[/tex] and [tex]cos90\°=0[/tex], [tex]sin90\° = 1[/tex]
Replacing,
[tex]tan(\frac{\pi}{2})=\frac{1}{0}[/tex]
Which is undetermined, because there is no number which product with zero isn't null.
Therefore, the solution is undetermined in this case.
